y-[y-(2-y)-1]=-(1-y)

Solution for y-[y-(2-y)-1]=-(1-y) equation:

Simplifying
y + -1[y + -1(2 + -1y) + -1] = -1(1 + -1y)
y + -1[y + (2 * -1 + -1y * -1) + -1] = -1(1 + -1y)
y + -1[y + (-2 + 1y) + -1] = -1(1 + -1y)

Reorder the terms:
y + -1[-2 + -1 + y + 1y] = -1(1 + -1y)

Combine like terms: -2 + -1 = -3
y + -1[-3 + y + 1y] = -1(1 + -1y)

Combine like terms: y + 1y = 2y
y + -1[-3 + 2y] = -1(1 + -1y)
y + [-3 * -1 + 2y * -1] = -1(1 + -1y)
y + [3 + -2y] = -1(1 + -1y)

Reorder the terms:
3 + y + -2y = -1(1 + -1y)

Combine like terms: y + -2y = -1y
3 + -1y = -1(1 + -1y)
3 + -1y = (1 * -1 + -1y * -1)
3 + -1y = (-1 + 1y)

Solving
3 + -1y = -1 + 1y

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-1y' to each side of the equation.
3 + -1y + -1y = -1 + 1y + -1y

Combine like terms: -1y + -1y = -2y
3 + -2y = -1 + 1y + -1y

Combine like terms: 1y + -1y = 0
3 + -2y = -1 + 0
3 + -2y = -1

Add '-3' to each side of the equation.
3 + -3 + -2y = -1 + -3

Combine like terms: 3 + -3 = 0
0 + -2y = -1 + -3
-2y = -1 + -3

Combine like terms: -1 + -3 = -4
-2y = -4

Divide each side by '-2'.
y = 2

Simplifying
y = 2